Headlights do not turn on at the light switch.

Your ignition switch is wired through a relay so the headlights will turn on automatically hope this helps

First I would suspect the dimmer switch on the steering column or wiring in the column. Second I would suspect a bad ground wire or ground connection. Here is link to a forum where others are having lighting problems with daylight running lights. The whole DRL system is rather a complicated maze of relays and connections, any of which could cause your problem. The tip on the forum to get a wiring diagram form Autozone looks like a good deal.

Headlight Wiring Diagram 02 F250 DRL Ford Truck Enthusiasts Forums

Normally this condition is the result of a poor body ground connection. Testing for this can be deceiving. At the static(nothing on) condition, testing can show a good ground. However when a circuit is excited, it has a determined resistance and a set current flow. If the ground connection to this or a branch circuit is loose, corroded, or broken wire. This will allow just enough connection to show as being good, but not good enough to complete the circuit with the required amount of connection when energized.

Might these be "driving lights"?
Cars with "driving lights" have lights that are supposed to stay on all the time the engine is running.
These lights not only look like headlights, in fact some cars even have the headlights themselves come on when the engine is running. Look as some more (several) 2002 Grand Marquis's and see if they are the same.
Be blessed.

My guess is that your running lights are staying on. There is a little black box (relay)or switch that keeps running lights on when you drive.
Check and replace with new one. Good luck.
PS There maybe a TSB on this issue.

All types of car headlight problem troubleshooting.Click the link below :---All headlights not working? http://repairhelpcenter.blogspot.com/2012/01/all-headlights-not-working.html
---------This will help.Thanks.

Daytime running light module!!!! $400.00 from the dealer..lol

Sounds like the headlight switch or connections to the switch are faulty.

your daytime running light module could be bad.there is also a headlight relay,and the switch could be bad,do the high beams work?click the switch a few times maybe it is jammed.

try checking the daytime running light module.
there is also a sensor for the auto headlights that may think it is still daylight.try playing around with the auto switch